Foundations of Geospatial Analysis
About Me
Professor of Urban Analytics & Current Head of Department @ Bartlett Centre for Advanced Spatial Analysis (CASA), UCL
Geographer by background - ex-Secondary School Teacher - back in HE for 15+ years
Taught GIS / Spatial Data Science at postgrad level for last 10 years
Where? (absolute)
Everything happens somewhere
- We’re here: Wallspace, 22 Duke’s Road, Camden, London, England, *Europe, Northern Hemisphere, Earth
Where? (absolute)
- How do we know exactly where?
Where? Coordinate Reference Systems
More reliable than names (that are rarely unique or reference fuzzy locations), are coordinates
The earth is roughly spherical and points anywhere on its surface can be described using the World Geodetic System (WGS) - a geographic (spherical) coordinate system
Points can be referenced according to their position on a grid of latitudes (degrees north or south of the equator) and longitudes (degrees east or west of the Prime - Greenwich - meridian)
The last major revision of the World Geodetic System was in 1984 and WGS84 is still used today as the standard system for references places on the globe.
Where? Coordinate Reference Systems
Projected Coordinate Reference Systems convert the 3D globe to a 2D plane and can do so in a huge variety of different ways
Most national mapping agencies have their own projected coordinate systems - in Britain the Ordnance Survey maintain the British National Grid which locates places according to 6-digit Easting and Northing coordinates
Every coordinate system can be referenced by its EPSG code, e.g. WGS84 = 4326 or British National Grid = 27700 with mathematical transformations to convert between them
Where? Describing and Locating Things with Coordinates
Once we have a coordinate reference system we can locate objects accurately in space
Most objects that spatial data scientists are concerned with (apart from gridded representations, which we will ignore for now!) can be simplified to either a point, a line or a polygon in that space
Polygons and lines are just multiple point coordinates joined together!
Where? Relative - Tobler’s First Law of Geography
“Everything is related to everything else, but near things are more related than distant things.”
This observation underpins much of what spatial data scientists do
Being able to locate something in space allows us to:
explain why something may be occurring where it is
make better predictions about nearby or further away things
Underpins the whole Geodeomographics (customer segmentation) industry!!
Where? Relative - Defining ‘near’ and ‘distant’
Near and distant can mean different things in different contexts
- the furthest one would travel to buy a pint of milk is somewhat different to furthest one might be willing to commute for a job
In spatial data science one way of separating near from distant can simply be to define their topological relationship - Dimensionally Extended 9-Intersection Model (DE-9IM) is the standard topological model used in GIS
Touching or overlapping objects = ‘near’
Where? Relative - Exploring Near and Distant
- If we measure the distance from the centre (centroid) of one ward to another, then we might decide that the 1st, 2nd, 3rd, kth. closest wards are near, the others are far.
Where? Relative - Exploring Near and Distant
- We can then decide to include the “k” nearest neighbours or exclude the rest
Where? Relative - Exploring Near and Distant
Other conceptions of near might include any contiguous ward with distant simply being those which are not contiguous
Near or distant could also be defined by some distance threshold
Spatial Autocorrelation
(Intercept) average_gcse_capped_point_scores_2014
190.2624075 0.4190508 
- If there is a linear correlation between the variable and its spatial lag, we can observe that values in near places do tend to cluster
Explaining Spatial Patterns
(Intercept)
371.71500
unauthorised_absence_in_all_schools_percent_2013
-41.40264 
Taking the whole of London, it would appear that there is a moderately strong, negative relationship between missing school and exam performance
For every 1% of additional school days missed, we might expect a decrease of -41 points in GCSE score.
But does this relationship hold true across all wards in the city?
Geographically Weighted Regression
GWR is a method for systematically running a series of localised regression analyses across a study area, collecting coefficients and other diagnostics for each zone of interest.
Something similar can be achieved through spatial sub-setting - i.e. running analyses for groups of zones within a higher level geography
Geographically Weighted Regression
Geographically Weighted Regression
In a GWR analysis, kernel weighting functions of different bandwidths (diameters) and shapes are used to include and weight or exclude neighbouring observations
Adaptive weighting can be used to adjust the size of the kernel according to some threshold of observations
For every point in the dataset a regression is run including the values within the kernel (which, of course, can only be achieved effectively through understanding the coordinate reference system of the observations)
